<p>We propose SL(2, ℤ) dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of boundary conditions for Abelian (quiver) ADHM theories and circular quiver Chern-Simons matter theories including the ABJM model. For the circular quiver Chern-Simons theories we take boundary conditions breaking a U(1)<sub>1</sub> × U(1)<sub>−1</sub> gauge group to its diagonal subgroup which is decoupled. This can be generalized to break U(1)<sub><i>k</i></sub> × U(1)<sub>−<i>k</i></sub>, leaving a ℤ<sub><i>k</i></sub> gauge theory. We find matching of the ’t Hooft anomalies and supersymmetric half-indices for all the proposed dual boundary conditions.</p>

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SL(2, ℤ) dualities of boundary conditions in Abelian M2-brane SCFTs

  • Tadashi Okazaki,
  • Douglas J. Smith

摘要

We propose SL(2, ℤ) dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of boundary conditions for Abelian (quiver) ADHM theories and circular quiver Chern-Simons matter theories including the ABJM model. For the circular quiver Chern-Simons theories we take boundary conditions breaking a U(1)1 × U(1)−1 gauge group to its diagonal subgroup which is decoupled. This can be generalized to break U(1)k × U(1)k, leaving a ℤk gauge theory. We find matching of the ’t Hooft anomalies and supersymmetric half-indices for all the proposed dual boundary conditions.